David has two cylinder shaped bottles of punch, each with a height of 12 inches and a radius of 2 inches. He wants to fill a half-sphere punch bowl to the brim with the punch. What should the radius of the punch bowl be to the nearest tenth of an inch to fill it entirely with the two bottles of punch?

5.2 inches

Step-by-step explanation:

Hi, first we have to find the volume of the cylinder shaped bottles:

V = π r^2 h

where:

V =volume

r= radius

h= height

Replacing with the values given:

V = π 2^2 (12)= 150.80 cubic inches

Since there are 2 bottles

Total punch: 2V = 301.59 cubic inches

The formula for the volume of a half-sphere is

V = (2 / 3) π r3.

Since the half-sphere is filled with the two bottles of punch (301.59 cubic inches)

301.59 =(2 / 3) π r3.

301.59/ (2/3) π =r3

144 =r3

∛144 =r

5.2 inches =r

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

hope this .

r3t40